{
 "cells": [
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "Numpy的数组 ndarray",
   "id": "d26cf420c8a6e34"
  },
  {
   "cell_type": "code",
   "id": "initial_id",
   "metadata": {
    "collapsed": true,
    "ExecuteTime": {
     "end_time": "2025-06-24T06:11:59.912489Z",
     "start_time": "2025-06-24T06:11:59.909532Z"
    }
   },
   "source": [
    "import numpy as np\n",
    "a=np.array([3,6,7])\n",
    "print(a,a.__class__,[3,6,7].__class__)"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[3 6 7] <class 'numpy.ndarray'> <class 'list'>\n"
     ]
    }
   ],
   "execution_count": 2
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "linspace",
   "id": "ba18b06adbe6fbfa"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-06-24T06:17:56.378080Z",
     "start_time": "2025-06-24T06:17:56.375379Z"
    }
   },
   "cell_type": "code",
   "source": [
    "import  numpy as np\n",
    "a=np.linspace(-30,30,20)\n",
    "print(a)"
   ],
   "id": "e001ca1027efd93f",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-30.         -26.84210526 -23.68421053 -20.52631579 -17.36842105\n",
      " -14.21052632 -11.05263158  -7.89473684  -4.73684211  -1.57894737\n",
      "   1.57894737   4.73684211   7.89473684  11.05263158  14.21052632\n",
      "  17.36842105  20.52631579  23.68421053  26.84210526  30.        ]\n"
     ]
    }
   ],
   "execution_count": 8
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "arange",
   "id": "4a226bfa4c3acd98"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-06-24T06:19:13.441951Z",
     "start_time": "2025-06-24T06:19:13.439634Z"
    }
   },
   "cell_type": "code",
   "source": [
    "import  numpy as np\n",
    "a=np.arange(-30,30,2)\n",
    "print(a)"
   ],
   "id": "c40c617a8db9341f",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-30 -28 -26 -24 -22 -20 -18 -16 -14 -12 -10  -8  -6  -4  -2   0   2   4\n",
      "   6   8  10  12  14  16  18  20  22  24  26  28]\n"
     ]
    }
   ],
   "execution_count": 9
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "随机数",
   "id": "d02bbae05e1738c3"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-06-24T06:31:57.138712Z",
     "start_time": "2025-06-24T06:31:57.135872Z"
    }
   },
   "cell_type": "code",
   "source": [
    "import numpy as np\n",
    "np.random.seed(9999)\n",
    "a= np.random.rand(2,8)*10+5\n",
    "print(a)"
   ],
   "id": "6715ebb71a7f7f44",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[13.23389074  7.18602745  5.31461009 10.45926167  6.5445562   6.86963293\n",
      "   9.22347694 11.055525  ]\n",
      " [ 9.92354112 11.44119068 14.13049479 12.71104109  7.88361219  9.15441344\n",
      "   8.31490435  8.66326695]]\n"
     ]
    }
   ],
   "execution_count": 15
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "ndarray 类型 相比 list好处",
   "id": "f1c7c3963777ddd4"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-06-24T06:40:17.238520Z",
     "start_time": "2025-06-24T06:40:17.235519Z"
    }
   },
   "cell_type": "code",
   "source": [
    "import  numpy as np\n",
    "a=np.arange(-30,30,2)\n",
    "b=[3,6,8]\n",
    "\n",
    "c=a*3+4\n",
    "print(a,c)\n",
    "print(a[0])"
   ],
   "id": "f4228d4f87925415",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-30 -28 -26 -24 -22 -20 -18 -16 -14 -12 -10  -8  -6  -4  -2   0   2   4\n",
      "   6   8  10  12  14  16  18  20  22  24  26  28] [-86 -80 -74 -68 -62 -56 -50 -44 -38 -32 -26 -20 -14  -8  -2   4  10  16\n",
      "  22  28  34  40  46  52  58  64  70  76  82  88]\n",
      "-30\n"
     ]
    }
   ],
   "execution_count": 18
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "ndarray shape",
   "id": "6b45a215d5310211"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-06-24T06:47:44.071757Z",
     "start_time": "2025-06-24T06:47:44.068639Z"
    }
   },
   "cell_type": "code",
   "source": [
    "import  numpy as np\n",
    "a=np.linspace(-30,30,20)\n",
    "print(a,a.shape)\n",
    "b=a.reshape(-1,1)\n",
    "print(b)\n",
    "print(b.reshape(20))"
   ],
   "id": "a159577bdcefa842",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-30.         -26.84210526 -23.68421053 -20.52631579 -17.36842105\n",
      " -14.21052632 -11.05263158  -7.89473684  -4.73684211  -1.57894737\n",
      "   1.57894737   4.73684211   7.89473684  11.05263158  14.21052632\n",
      "  17.36842105  20.52631579  23.68421053  26.84210526  30.        ] (20,)\n",
      "[[-30.        ]\n",
      " [-26.84210526]\n",
      " [-23.68421053]\n",
      " [-20.52631579]\n",
      " [-17.36842105]\n",
      " [-14.21052632]\n",
      " [-11.05263158]\n",
      " [ -7.89473684]\n",
      " [ -4.73684211]\n",
      " [ -1.57894737]\n",
      " [  1.57894737]\n",
      " [  4.73684211]\n",
      " [  7.89473684]\n",
      " [ 11.05263158]\n",
      " [ 14.21052632]\n",
      " [ 17.36842105]\n",
      " [ 20.52631579]\n",
      " [ 23.68421053]\n",
      " [ 26.84210526]\n",
      " [ 30.        ]]\n",
      "[-30.         -26.84210526 -23.68421053 -20.52631579 -17.36842105\n",
      " -14.21052632 -11.05263158  -7.89473684  -4.73684211  -1.57894737\n",
      "   1.57894737   4.73684211   7.89473684  11.05263158  14.21052632\n",
      "  17.36842105  20.52631579  23.68421053  26.84210526  30.        ]\n"
     ]
    }
   ],
   "execution_count": 29
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "绘图",
   "id": "57d7e7193371536f"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-06-24T07:08:37.236488Z",
     "start_time": "2025-06-24T07:08:37.175658Z"
    }
   },
   "cell_type": "code",
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "x=[2,5,7]\n",
    "y=np.array([4,5,7])\n",
    "plt.title(\"xxxx\")\n",
    "plt.scatter(x,y)\n",
    "plt.plot(x,y)\n",
    "plt.show()"
   ],
   "id": "4a2a1253e11e5e04",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 35
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "y= x**3  y=kx+b\n",
   "id": "8ee1cb52551e34dd"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-06-24T07:19:16.152576Z",
     "start_time": "2025-06-24T07:19:16.093317Z"
    }
   },
   "cell_type": "code",
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "x=np.linspace(-10,10,20)\n",
    "y=(x+1)**3+1\n",
    "# y=np.power(x,3)\n",
    "y_1=44*x+11\n",
    "plt.title(\"functions\")\n",
    "plt.plot(x,y)\n",
    "plt.plot(x,y_1)\n",
    "plt.show()"
   ],
   "id": "99880016ac66cb08",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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27bb3v379+m2zPjdTKBRwc3MzehAREVmjd/dcBADc1zsAHs72EldjGiYJM2FhYfDz88Pu3bv1z6lUKuzfvx+DBg0CAMTExMDOzs5om5ycHJw9e1a/TWxsLIqLi3Hs2DH9NkePHkVxcbF+GyIiIqrfkSsF+O1iPuxsZHhuRLjU5ZhMs++YU1ZWhkuXLuk/T01NxalTp+Dh4YHg4GDMnTsXy5cvR3h4OMLDw7F8+XI4OTlh2rRpAAClUonHH38c8+fPh6enJzw8PPDiiy+iR48eGDVqFAAgKioK48aNw+zZs/HJJ58AAP72t78hLi4OERERLdlvIiKidk0Igbd2pgAAHukXhCAPJ4krMp1mh5kTJ05g+PDh+s/nzZsHAJg5cybWrVuHl156CZWVlXjmmWdQWFiIAQMGYNeuXXB1ddW/5p133oGtrS0efvhhVFZWYuTIkVi3bh1sbGz023z11Vd4/vnn9V1PkyZNavDeNkRERKSz/8J1nLhaCIWtvF3PygCATAghpC7C1EpKSqBUKlFcXMzrZ4iIqN0TQmDS+7/jTFYxnrg3DK/FdZO6pGZp7N9vrs1ERETUzuw8l4szWcVwtrfB08M6S12OyTHMEBERtSMarcDbuy4AAP56bxg8XRQSV2R6DDNERETtyJbT2biYVwY3B1s8MaST1OW0CYYZIiKidkKt0eKdPbpZmSeHdobS0U7iitoGwwwREVE78UNCJq4WVMDLxR6zBoVKXU6bYZghIiJqB6rUGvzfL7q7/T49rAucFc2++4rFYZghIiJqB745lo6c4ir4Kx3w5wHBUpfTphhmiIiILFyFqgYf7NXdlf+5EeFwsLO5yyvaF4YZIiIiC7fuUBryy1QI9nDCQ30DpS6nzTHMEBERWbDiSjU+2X8FADB3VDjsbKzvT7v17TEREVE7suZgKoor1Qj3ccHk3h2lLkcSDDNEREQW6ka5Cmt+083KzBvdFTZymcQVSYNhhoiIyEJ9vP8yylUadA9ww9juflKXIxmGGSIiIgt0raQK6w+lAQBeHBMBuZXOygAMM0RERBbpg72XUF2jRUyIO4ZFeEtdjqQYZoiIiCxMxo0KfHMsHYBuVkYms95ZGYBhhoiIyOL83y8XodYIDO7iidjOnlKXIzmGGSIiIgty+XoZfjyZCUA3K0MMM0RERBbl3T0XoRXAqCgf3BPsLnU5ZoFhhoiIyEIk5ZRgy+lsAMC80ZyVqcMwQ0REZCHe3nUBABDX0x/dAtwkrsZ8MMwQERFZgMT0QuxJuga5DJg7qqvU5ZgVhhkiIiILsHq3blZmSp9AdPFxkbga88IwQ0REZOaOXCnAbxfzYWcjw99HhktdjtlhmCEiIjJjQgi8tTMFADC1XzCCPJwkrsj8MMwQERGZsX0XruPE1UIobOWYM6KL1OWYJYYZIiIiMyWEwNu7dLMyM2JD4OvmIHFF5olhhoiIyEztPJeLs1klcLa3wdPDOCvTEIYZIiIiM6TRCv19ZR6/NwwezvYSV2S+GGaIiIjM0ObTWbiYVwY3B1s8PqST1OWYNYYZIiIiM6PWaPHunosAgCeHdobS0U7iiswbwwwREZGZ+SEhE1cLKuDlYo+/DA6VuhyzxzBDRERkRqrUGvzfL7pZmWeGdYGTva3EFZk/hhkiIiIz8vXRdOQUV8Ff6YBpA4KlLsciMMwQERGZiQpVDT7cdwkA8NyIcDjY2UhckWVgmCEiIjIT6w6lIb9MhRBPJzzUN1DqciwGwwwREZEZKK5U45P9VwAAc0eFw86Gf6Ibi98pIiIiM7DmtysorlQj3McFk3p1lLoci8IwQ0REJLEb5SqsOZgKAJg3uits5DKJK7IsDDNEREQS+3j/ZZSrNIju6IZx0X5Sl2NxGGaIiIgkdLWgHOsPpQEA5o+JgEzGWZmmYpghIiKSiFYr8PKPf6C6RovBXTwxrKu31CVZJIYZIiIiiXx9LB1HrtyAo50NVk7pyVmZZmKYISIikkBmYQVWbE8CALw8LgJBHk4SV2S5GGaIiIjamBACCzeeQblKg74h7pgRGyp1SRaNYYaIiKiNfZ+Qid8u5kNhK8eqB3tCzlbsFmGYISIiakPXSqrwr63nAejuKdPJ20XiiiwfwwwREVEbEULg1U1nUFpVg15BHfDEkE5Sl9QuMMwQERG1kc2ns7EnKQ92NjK8+WBP3um3lTDMEBERtYHrpdVYtPkcAOD5EeHo6usqcUXtB8MMERFRG1i8+RyKKtTo5u+Gp4Z1lrqcdoVhhoiIyMR+PpODbWdyYCuXYdWDPWFnwz+/rYnfTSIiIhMqLFfhf/6rO7309LDOiO6olLii9odhhoiIyISWbj2P/LJqhPu4YM6ILlKX0y4xzBAREZnIL0nXsCkxC3IZsOrBnlDY2khdUrvEMENERGQCxZVqvLLpDADgiSGdcE+wu8QVtV8MM0RERCawYnsSrpVUI8zLGfNGd5W6nHaNYYaIiKiV/XbxOjYcz4Cs9vSSgx1PL5kSwwwREVErKquuwYIfdaeXZsaGol+oh8QVtX8MM0RERK1o1Y5kZBVVItDdEf8YGyF1OVaBYYaIiKiVHL1SgM8PXwUAvPFATzgrbCWuyDowzBAREbWCSpUGL//4BwDg0f5BGNzFS+KKrAfDDBERUSt4e1cK0goq4K90wMIJUVKXY1UYZoiIiFroZHoh1vyeCgBYfn8PuDnYSVyRdWGYISIiaoEqtQYv/fAHhACm9OmI4ZE+UpdkdRhmiIiIWuC9Xy/iUl4ZvFwU+GdcN6nLsUoMM0RERM10NqsYH++/AgB4/b5odHCyl7gi68QwQ0RE1AyqGi1e/P40NFqBuJ7+GBftJ3VJVothhoiIqBk+2ncZybml8HC2x5JJ3aUux6oxzBARETVRcm4J3t97EQCweFJ3eLooJK7Iupk0zCxevBgymczo4ednmIYTQmDx4sUICAiAo6Mjhg0bhnPnzhm9R3V1NZ577jl4eXnB2dkZkyZNQmZmpinLJiIialCNRouXfvgDao3A6G6+iO/pL3VJVs/kMzPdu3dHTk6O/nHmzBn92KpVq7B69Wq8//77OH78OPz8/DB69GiUlpbqt5k7dy42bdqEDRs24ODBgygrK0NcXBw0Go2pSyciIrrNfw6m4o/MYrg52GLZfdGQyWRSl2T1TL5ohK2trdFsTB0hBN599128+uqrmDJlCgBg/fr18PX1xddff40nn3wSxcXFWLNmDb744guMGjUKAPDll18iKCgIe/bswdixY01dPhERkd6lvDKs3n0BAPDP+O7wcXOQuCIC2mBm5uLFiwgICEBYWBimTp2KK1d0LWypqanIzc3FmDFj9NsqFAoMHToUhw4dAgAkJCRArVYbbRMQEIDo6Gj9NvWprq5GSUmJ0YOIiKglNFqBl344DVWNFkO7euOBPh2lLolqmTTMDBgwAJ9//jl27tyJf//738jNzcWgQYNQUFCA3NxcAICvr6/Ra3x9ffVjubm5sLe3h7u7e4Pb1GfFihVQKpX6R1BQUCvvGRERWZv1h9JwMr0ILgpbLJ/Sg6eXzIhJw8z48ePxwAMPoEePHhg1ahS2bdsGQHc6qc6tPwxCiLv+gNxtm4ULF6K4uFj/yMjIaMFeEBGRtbtaUI5VO5MBAAsnRKJjB0eJK6KbtWlrtrOzM3r06IGLFy/qr6O5dYYlLy9PP1vj5+cHlUqFwsLCBrepj0KhgJubm9GDiIioOarUGrzw7SlUqbWI7eSJR/sFS10S3aJNw0x1dTWSkpLg7++PsLAw+Pn5Yffu3fpxlUqF/fv3Y9CgQQCAmJgY2NnZGW2Tk5ODs2fP6rchIiIyFa1W4B8//IGT6UVwdbDFGw/0hFzO00vmxqTdTC+++CLi4+MRHByMvLw8vP766ygpKcHMmTMhk8kwd+5cLF++HOHh4QgPD8fy5cvh5OSEadOmAQCUSiUef/xxzJ8/H56envDw8MCLL76oP21FRERkSu/suYAtp7NhK5fhk8diEOzpJHVJVA+ThpnMzEw8+uijyM/Ph7e3NwYOHIgjR44gJCQEAPDSSy+hsrISzzzzDAoLCzFgwADs2rULrq6u+vd45513YGtri4cffhiVlZUYOXIk1q1bBxsbG1OWTkREVu77Exl479dLAIDlU3pgUBcviSuihsiEEELqIkytpKQESqUSxcXFvH6GiIju6tClfMz47BhqtAJzhnfBi2MjpC7JvGnUAGSATevOkTT27zfXZiIiIrrJpbxSPPVlAmq0AvG9AjBvdFepSzJP6kogeRuw6WngzS7Apd13f42JmPwOwERERJYiv6waf1l3HCVVNYgJccebD/KCXyNVxcCFXUDSZuDSHkBdYRi7uBuIGC9JWQwzRERE0LVgz/78BDJuVCLE0wmfTo+Bgx2vz0RZnm4GJnkrcGU/oFUbxpRBQGQcEBUPBA+UrESGGSIisnparcD8704jMb0ISkc7fDarHzxdFFKXJZ3Cq7rwkrQFSD8C4KbLa70idOElKg7w7w2YwZ2QGWaIiMjqvbkrBdvO5MDORoZPpsegs7eL1CW1LSGA68m68JK0Bcj9w3g8oI8uvETGA97mdw0RwwwREVm1DcfS8dG+ywCANx7oiYGdPCWuqI1otUD2SUOAuXHZMCaTAyGDdTMwkRMBZaB0dTYCwwwREVmt3y5ex6s/nQUA/H1kOKb0Me8/2i2mqQGu/q4LL8nbgNJsw5iNPdB5hO4amIjxgLPl3FeHYYaIiKzShWuleObLk9BoBe6/pyPmjgqXuiTTUFcCl/fqroFJ2Q5U3rTeob0LED5GNwMTPhpQuDb8PmaMYYaIiKxOXmkV/rL2OEqra9A/1AMrH+gBmRlcyNpqqop1rdJJm4GLewB1uWHMyROImKALMGFDATsH6epsJQwzRERkVSpVGsxefwJZRZUI83LGJ9NjoLBtBy3YZdeBlG1A0lbgyj7jFmq3QN0FvFHxQNDAVr9Tr9Ta194QERHdgVYrMPfbRJzOLIa7kx3WzuoHd2d7qctqvqJ0XXhJ2gJkHAGE1jDm1bX2At44IOAes2ihNhWGGSIishordyRj57lrsLeR49MZfRHq5Sx1SU0jBHA9pfYC3i1Azmnj8YB7DDex87ae9aQYZoiIyCp8eeQqPj1wBQDw5kM90S/UQ+KKGkkIIOukLrwkbQEKLhnGZHIgeJChhbpDkHR1SohhhoiI2r19KXlYtPkcAGD+6K6Y3LujxBXdhaYGSD9kaKEuyTKM2dgDnYbrroGJmGBRLdSmwjBDRETtWlJOCeZ8nQiNVuCBPoGYM6KL1CXVT10FXNmruwYmZTtQecMwZu+ia52Oige6jAYc3KSr0wwxzBARUbt1raQKf113HGXVNRjYyQMrpphZC3ZVCXBxl24G5tIeQFVmGHP0ACIn6JYQ6DSsXbRQmwrDDBERtUsVqho8vv44coqr0MnbGZ881hf2tnKpy6ptod5euwr1PkCjMoy5dbxpFerYdtdCbSr8LhERUbuj0Qo8/80pnM0qgaezPdbN6g+lk510BdW1UCdvBdIPG7dQe4YbVqEO6NOuW6hNhWGGiIjanWXbkrAn6RrsbXUt2MGeTm1bQF0LdV0H0q0t1P69awOMdbVQmwrDDBERtSvrD6Xhs99TAQCrH+6FmBD3tvnCRi3UW4GCi4YxfQt1XG0LdXDb1GQlGGaIiKjd+DX5GpZs0bVgvzQuAnE9A0z7Be/aQj1MN/vCFmqTYpghIqJ24Vx2MeZ8nQitAB7pG4Snh3Y2zRfSt1BvAVJ+Nm6htnMGuo7RXcQbPoYt1G2EYYaIiCxedlEl/rruOCpUGgzu4onX749u3Rbsm1uoL+42XoXa0R2ImKibgWELtSQYZoiIyKKdzSrG4+uP41pJNcJ9XPDhn2NgZ9MKLdh1LdRJW4DU/cYt1K4BhlWogwexhVpi/O4TEZHF2nP+Gp7fkIgKlQbhPi5Y99f+UDq2oAX7ji3UXWrXQIrXLegoN4N71hAAhhkiIrJAQgh89nsaXt92HkIAQ8K98P60Pk0PMndtoe5lCDDeEbwHjJlimCEiIotSo9FiyZbz+OLIVQDAo/2DsXRy98afWhICyD6pCy+3tlBDBoQM0l3AGzkRcA9p/R2gVscwQ0REFqO0So05Xydi/4XrkMmAV8ZH4YkhYXe/2FffQl17CunmFmq5nXELtYu3SfeBWh/DDBERWYTMwgo8vu4EUq6VwtHOBu9O7Y2x3f0afoG6Srf2UdKW21ehtnM2rEIdPhpwUJq8fjIdhhkiIjJ7pzOK8Pj6E8gvq4aPqwJrZvZDj8B6AkhdC3XyVl0LtdEq1O66mRd9C7Vjm9VPpsUwQ0REZu3nMzl44btTqFJrEennis9m9UNAh5uCSHm+oYX61lWo61qoI+OAkMFsoW6neFSJiMgsCSHwyYErWPlzMgBgeIQ33pvWBy4KW6AoQzf7krRVdy3MzS3UHp1rF3GcxBZqK8EwQ0REZket0eK1TWfx7YkMAMCsQaF4rb8ctkffrW2hPmX8Ar+eN61CHckWaivDMENERGaluEKNp79KwKHL+eglT8W/ul5Bz/SDwMkLN20lA4JjDaeQ2EJt1RhmiIjIbKRfL8G7n63H6NLf8LbiBPxlBUBa7aDcDug09KYWah8pSyUzwjBDRETSqm2hzj/xI1wv7sBqlBj+Otk56VqnI+N1q1GzhZrqwTBDRERtr7rUeBVqVRm8aodKZK6wi5oAx573AZ2Hs4Wa7ophhoiI2kZ5wU0t1HuNWqhzhTt2avoiP2gMnp4xHY6ODDDUeAwzRERkOsWZhiUErv5u1EKtde+EffIB+L/sKJwWnfDEkM5YMD4KNnJ2IlHTMMwQEVHrun7BsAp1dqLxmF8PIGoSikPGYvbP5Th2tRA2chlev687/jyAHUnUPAwzRETUMkLoQkvdTezyU24alAHBA3UdSJETAfdQXLlehr+uO460ggq4KmzxwZ/74E9dubgjNR/DDBERNZ1WA6Qf1s2+JG8DijMMY3Ut1JFxugBzUwv1kSsFePKLBBRXqtGxgyPW/qUfuvq6SrAD1J4wzBARUePUVBuvQl1RYBizcwK6jNItIdBAC/UPCZlYuPEPqDUCvYM64N8z+sLbVdF29VO7xTBDREQNqy7VtU7rW6hLDWMOHWpXoY4DOo9osIU6vaAC/9p2HrvPXwMATOzhj7cf7gUHO5s22AGyBgwzRERkrK6FOnkrcHkvoKk2jLn6604fRdWtQm3X4NtUqjT4aN8lfHzgClQ1WtjIZXh2eBfMHRkOOTuWqBUxzBARka6FOnmbbgbmlhZqeHS6aRXqPnddhVoIgZ3ncvGvrUnIKqoEAAzu4onF8d0RzutjyAQYZoiIrFX+RV14SdoCZJ80HqttoUZkHOAT1ehVqC/llWLx5vM4eCkfABCgdMBrcd0wPtoPMq5kTSbCMENEZC2EAHJO6dqnk7bU30JddwrJPbRJb11apcb//XIRa39PQ41WwN5Wjqf+1AlPD+sCR3teG0OmxTBDRNSeaTVA+pHaFuqtjW6hbvTbawU2JWZh5Y5kXC/VXVszKsoX/4zrhmBPp9baC6I7YpghImpvaqqBK/t1d+FN3g5U5BvGbm6hDh8NOHZo9pc5m1WMRZvPIeFqIQAgzMsZ/4zvhuERTQ9FRC3BMENE1B5UlwGXaluoL+xqVgt1YxWWq/DmrhR8cywdQgBO9jZ4bkQ4/npvKBS2PKVEbY9hhojIUlXcqF2Feitw+dd6Wqgn6rqQ7tJC3VgarcDXx9Lx9q4UFFWoAQCTegXglQlR8FM6tPj9iZqLYYaIyJIUZ9W2UG8Grh4ChMYwVtdCHRkPdIy5awt1U5xIu4F//vcczueUAAAi/VyxeFJ3DOzk2Wpfg6i5GGaIiMxd/iVdeEneCmQlGI/59dCFl6j4JrVQN1ZeSRVW/JyMTYlZAAA3B1vMHxOBPw8Ihq1N64UlopZgmCEiMjdCADmna1eh3gJcT75pUAYEDai9iV3TW6gbS1WjxbpDqfjfPRdRrtJAJgMe6RuEf4yNgKcL11Mi88IwQ0RkDrQaIONo7U3stgLF6YYxuS0QNlQXXiImAq6+Ji3lwIXrWLzlHK5cLwcA9ArqgKWTuqNXUAeTfl2i5mKYISKSSk01kHrAsAp1+XXDmK0jED5Kdwqp69gWtVA3VnpBBZZtP4+d53QLQno62+Pl8ZF4sE8g11Iis8YwQ0TUlqrLgEt7aleh3gVUlxjGHJRA1/G6U0idRwD2pr/pXJVag53ncvH9iUz8fjkfQgA2chlmxIZg7qiuUDq2vAuKyNQYZoiITK3iBpDys+4amEu/GLdQu/galhAIHdIqLdR3I4RAYkYRvj+Ria2ns1FaXaMfGxLuhdcmdkOEHxeEJMvBMENEZAol2YYW6rTfjVuo3UMNq1B37NuqLdR3cq2kChtPZuGHhAxcrr0eBgA6dnDEgzGBeKBPIJcgIIvEMENE1FryL+mWEEjacnsLtW907T1g4gDf7q3eQt2QKrUGe5Ku4YeETBy4cB1aoXvewU6OCdH+eLBvIAaGefKaGLJoDDNERM0lBJD7h6ED6XqS8XjQAMMpJI9ObViWwJmsYnx/IhObT2ejuFKtH+sX6o4HYwIxoYc/XB14PQy1DwwzRERNoW+h3qqbhSm6pYU6dEjtDMxEwNWvTUu7XlqNnxKz8ENCJlKuGdZm8lc64IE+gXggJhBhXs5tWhNRW2CYISK6mxpVbQv15vpbqLuM1AWYrmMBR/c2LU1Vo8WvyXn4ISEDe1OuQ1N7HsneVo5x3f3wYEwgBnfxgg1PI1E7xjBDRFSfuhbq5K3AhZ0NtFDHAZ1HtkkL9a3OZRfjh4RM/PdUNm6Uq/TP9w7qgIf6BiKuZwDbqslqMMwQEdWpuAFc2KG7Bubyr0BNlWHMxVd36iiytoXa1r5NSxNCIP1GBX5NzsP3JzL1Cz4CgLerAlP6dMRDMYHo4sOWarI+DDNEZN30LdRbgLSD9bdQR8YDgf3arIUaAArKqnE6swinMopxOqMIpzOLUFRhuJDX3kaOUd188FBMEIaEe3HRR7JqDDNEZH0KLtd2IG0Bsk4Yj/lG13YgxbdZC3WFqgZns0pwOqMIpzKLcDqjCJmFlbdtZ28jR3RHN0zu3RGTegXA3bltZ4eIzBXDDBG1f0IAuWd04SV5K5B33ng8sL9hFWoTt1DXaLS4mFemn205lVGMC9dK9Rfu3qyztzN6BXVA76AO6BXYAZH+rlDY2pi0PiJLxDBDRO2TVgNkHNOFl6TNDbRQ165C7eZvkhKEEMgsrMTp2tmW0xnFOJNVjEq15rZtfVwVutBSG156BCrhxvvAEDUKwwwRtR81KiDtQO09YLYB5XmGMRO2UGu1AoUVKlwvq0ZOURXOZBmuc8kvU922vYvCFj0DlehVO+PSO6gD/JQOrVYPkbWxmDDz4Ycf4s0330ROTg66d++Od999F0OGDJG6LCKSmqpct3hj0pbaFupiw5hCCUSM010D02UkYN/4G8YJIVCu0uB6afVNjypcL7vp89qP88tU9Z4mAgBbuQxR/m7oFaRE7yB39A5SopOXC5cPIGpFFhFmvv32W8ydOxcffvghBg8ejE8++QTjx4/H+fPnERwcLHV5RNTWKguBlB2GVahrbrpY1tlH10IdFW/UQi2EQI1GC1WNFkWV6ltCSjWul1Xpg0ndc/WdDroTD2d7eLsoEOXvqpt1CeqAbv5ucLDjdS5EpiQTQtT/zwkzMmDAAPTp0wcfffSR/rmoqCjcd999WLFixV1fX1JSAqVSieLiYri5uZmyVCKLUaPRQqXRolqt+6+qRovqGg2qa+o+1v1X/7FGo/9YrRG4+VdH3YcC4pbP7zxueL3x8xohoNbovo6qRgu1RgvHqjxEFP+G6OIDCK88BVsYgkau3A+H7GNxwGYAzqArqjSy2tdra18voNJom/V9cra3gberwvBwUdzyuQO8XRXwdLGHHdujiVpVY/9+m/3MjEqlQkJCAhYsWGD0/JgxY3Do0KF6X1NdXY3q6mr95yUlJfVuR2TJqtQa5JVUI7ekCteMHtXIK61Cpao2mNQTWFQ1WjRwVsSshMhyMVZ+HJNsjqOP/JLRWJI2CDu1/bBT0w9JIhioqDttU3X7G93CzkZWTygxfOzlYvivs8Lsf00SWT2z/780Pz8fGo0Gvr6+Rs/7+voiNze33tesWLECS5YsaYvyiFpdjUaL/DLVbQGlLrTUBZibV0JuKRu5DApbOext5bC3kUNhp/uvva0N7G3lUNQ+6sZs5XLUXfIhq70Pi/4KkLrnaz+QyYyevunzW8ZlAISAX9Vl9Cg5gO4lB+BbedmozmvKnsjwGYls/1GodgtBmK0cz9nIYWcjh52NTF+/Xe3D3lam/9jORjdmayODk72Nvm4isnxmH2bq3PqLRwjR4C+jhQsXYt68efrPS0pKEBQUZNL6iBqrQlWDPzKLkV5QgWslVbUhpVofXPLLqhs9a+JgJ4efmwN83Bzg5+YAXzcFfGs/d7avCyI2+j/yRsHkpjFJFyHUaoHMY4ab2BVdNYzJbYHQe3XXv0RMhK+bP3wbficislJmH2a8vLxgY2Nz2yxMXl7ebbM1dRQKBRQKRVuUR3RHdfcZOZleiJNXC5GQXoiknPpvkHYzG7kMPq6K2pCiCyiGh0IfYNwcbC1zhqFGBaT9pgsvKduBsmuGMVsH3eKNdS3UTh7S1UlEFsHsw4y9vT1iYmKwe/du3H///frnd+/ejcmTJ0tYGdHtqms0OJddogsutY+80urbtvNzc0CEn6thNkXpAF9XB/gpHeDjpoCns0La2RJTqGuhTt6q60S6tYW661hdgGliCzURkdmHGQCYN28epk+fjr59+yI2Nhaffvop0tPT8dRTT0ldGlm5vNIqnLxahJPpuuByJqsYqhrjrhlbuQzdA9zQJ8QdfYLdERPijoAOjhJV3MYqC3X3fknacocW6jgg9E9tvgo1EbUfFhFmHnnkERQUFGDp0qXIyclBdHQ0tm/fjpCQEKlLIytSo9Ei5VqpYdYlvRAZN25fDNDD2V4fWvoEd0DPwA5wtLei+4yU5tYuIbBVdypJW2MY6xBSuwZS3SrUVvR9ISKTsYj7zLQU7zNDzVFcocbJjEJ9eDmVUYQKlfFN1GQyIMLXFX1C3BET7I4+Ie4I9XSyzOtYWuLGFV14SdoCZB6H4Q4zAHy66cJLZBzg16NNVqEmovah3dxnhqgtVao02PpHNjYcz0DC1cLbxl0Vtugd3KF21sUdvYM7WOdigEIA184ZVqG+dtZ4PLCfLrxExQOenaWpkYisBsMMEYBz2cXYcCwDP53KQmmV4bRImJcz+gS7o0+ILsCE+7i2vwtzG0ur1c26JG/RzcIUphrGZDaGFurIiYBbgHR1EpHVYZghq1VeXYMtp7PxzbF0nM40dNYEezjhkX5BeKBPIFcy1qiB1AO62ZfkbQ20UMcBXcexhZqIJMMwQ1ZFCIEzWcX45lgGNp/KQnntNTB2NjKM6e6HR/sFY1BnT+te0VhVAVz+RTf7cuFnoOrmFmo3XQt1ZBwQPpot1ERkFhhmyCqUVKnx31PZ2HAsHeeyDWt1hXk549H+QZjSJxBeLlZ8o8XKotoW6s31tFB7604dRcYDYWyhJiLzwzBD7ZYQAifTi7DhWDq2/pGDSrVuFsbeVo7x0X54tH8wBoR5WF/nUZ3SXN2po6Qt9bRQB+vCS1Q8ENSfLdREZNYYZqjdKa5QY2NiJjYcy0DKtVL98+E+LpjaPxhT7ukId2crnV2oa6FO3gpkHMNtLdR1HUhsoSYiC8IwQ+2CEALH0wrxzbF0bD+Tg+rau/A62MkxsUcApg0IQp9gd+ubhalroU6uvQfMrS3UHfvqLuCNjAe8ukhTIxFRCzHMkEW7Ua7CxpOZ+OZYOi5fL9c/H+nnimkDgjG5d0coHa3sPjBaLZB1Qnf9S70t1IOBqElsoSaidoNhhixSSm4p3t97CTvP5kKl0c3CONnbYFKvAEztH4xegUrrmoXRqGtXoa5rob5plXlbB6DzCN0ppIjxbKEmonaHYYYsSoWqBv+75yLWHExFjVZ3vUePjko82j8Yk3oHwEVhRT/Sqgrg8q+600d3aqHuMgpQuEhXJxGRiVnRb36ydLvO5WLJlvPIKtK1DY/t7ovnRoQjuqNS4sraUF0LdfIW4OKe21uoIyboTiGFDQFsrbjVnIisCsMMmb3Mwgos3nwee5J0d5/t2MERSyd3x8goX4krayOl14CU2hbq1APGLdTK4NpVqOOAoAFsoSYiq8QwQ2ZLrdFizcFU/O+ei6hUa2Arl+Fvf+qE50aEw9G+nf/RvpFa24G0Fcg4CqMWau8oXXiJigf8erKFmoisHsMMmaVjqTfw2k9ncOFaGQCgf5gHlt0XjXBfV4krMxEhgLzzuvCStAW4dsZ4vGNM7SKObKEmIroVwwyZlRvlKqzYnoTvEzIBAB7O9nhlQhQe6NOx/XUnabVAVoKuhTp5q+6GdnXqWqgja1ehVnaUrk4iIjPHMENmQasV+D4hAyt+TkZRhRoA8Gj/ILw8LhIdnNrR3Xo1aiDtoGEV6tIcw5iNQtdCHRXPFmoioiZgmCHJJeeW4LVNZ3HiaiEA3Q3vlt0fjZiQdvLHXF1paKFO+RmoKjKM2bvqWqij4oAuo9lCTUTUDAwzJJlb7xnjZG+DeaO7YtagUNjayKUur2Uqi4CLu3QB5tIeQF1hGHPyAiIn6E4hdRrKFmoiohZimCFJ3HrPmHHd/fDP+G4I6OAocWUtUJZnWIU69QCgVRvGlEG1F/DGAcED2UJNRNSKGGaoTd16z5hAd909Y0ZEWug9YwrTDKtQpx+BcQt1pGEVav9ebKEmIjIRhhlqE7feM8bORobZQyzwnjFCAHlJtfeA2Qzk3tJCHdCn9iZ28YBXuDQ1EhFZGYYZMjmLv2eMVgtknzSsQn3jsmFMJgdCBteeQpoIKAOlq5OIyEoxzJDJWPQ9YzQ1wNWDhlNIt7VQD9cFmK7jAWdP6eokIiKGGTKNQ5fz8exXJ1FoSfeMUVcCl/caVqGuLDSM2bsCXcfoAkyXUYDCQmaViIisAMMMtbr/nsrCi9+fhlojzP+eMVXFwIVdhlWo1eWGMSdPwyrUbKEmIjJbDDPUaoQQ+Hj/FbyxIxkAMLGHP95+uBcc7MzsAt+yPCBlu24G5sr+21uo6zqQ2EJNRGQRGGaoVWi0Aos3n8MXR64CAJ64NwyvTIiCXG4m18YUXjWsQp1+GEYt1F4RhlWo/XuzhZqIyMIwzFCLVao0eH5DInafvwaZDHhtYjc8fm+YtEUJAVxP1s2+JG0Bcv8wHg+4x7AKtXdXaWokIqJWwTBDLVJQVo3H15/AqYwi2NvK8e4jvTGhh780xehbqGsDTH0t1JFxuhbqDkHS1EhERK2OYYaaLS2/HLPWHkNaQQWUjnb4z8y+6Bfaxhf6amqAq7/rwkvyNqA02zBmY69bhToyTrcKtbNX29ZGRERtgmGGmiUxvRCPrz+BG+UqBLo7Yt1f+qOLTxut+FzXQp28VXchr1ELtQsQXttCHT6aLdRERFaAYYaabPf5a3jum5OoUmsR3dENn83qBx9XB9N+0api4OJu3V14G2yhjgfChgJ2Jq6FiIjMCsMMNcmXR67in/89C60Ahnb1xod/7gNnhYl+jMquAynbdB1IV/YZt1C7Bequfek2CQgaCNjwR5mIyFrxLwA1ihACb+5MwYf7dBfVPtI3CK/fHw07G3nrfqGidF14SdoCZBwBhNYw5tW1tgMpTteNxBZqIiICwww1gqpGi5d+OI2fTukurn1hVFc8P7JL66yvJARwPaX2At4tQM5p43H/3oZVqL0jWv71iIio3WGYoTsqqVLjqS8ScOhyAWzkMqyY0gMP921hW7MQQNZJXXhJ2gIUXDKMyeRA8CDDKtRsoSYiortgmKEG5RRX4i9rjyM5txTO9jb48LEYDO3q3bw309QA6YcMLdQlWYYxG3ug03DdXXgjJrCFmoiImoRhhuqVnFuCWZ8dR25JFbxdFVg7qx+iOyqb9ibqKuDKXt01MCnbgcobhjF7F13rdFQ80GU04ODWujtARERWg2GGbnPoUj6e/CIBpdU16OLjgnV/6YdAd6fGvbiqBLi4SzcDc2kPoCozjDl6AJETdEsIdBrGFmoiImoVDDNk5L+nsvDi96eh1gj0D/XApzNi0MHJ/s4vKruum3lJrm2h1qgMY24db1qFOpYt1ERE1Or4l4UA6FqvP9p/Gat2pAAAJvbwx9sP94KDnU39L6hroU6uXYX65hZqz3DDKtQBfdhCTUREJsUwQ9BoBRZtPosvj6QDAJ64NwyvTIiCXH5TCKlroa7rQKq3hToOiJrEFmoiImpTDDNWrlKlwXPfJGJP0jXIZMBrE7vh8XvDdINGLdRbgYKLhhfK5LrTRvoW6mBpdoCIiKwew4wVKyirxuPrT+BURhHsbeV495HemNDNG0g9cIcW6mG1q1BPAFya2aZNRETUihhmrFRhuQoPfXwYV/LL4e0g8NXIUnS9/Dqw/ZYWajtnQwt1+Bi2UBMRkdlhmLFCqhotXvj8AKJv7MWrTicx3OY05L/ctAq1ozsQMVF3DUynYYCdo2S1EhER3Q3DjDUpuw6Rsh2p+77GJyUnoLCvAbTQPVwDDB1IwYPYQk1ERBaDf7Hau1taqGVCiwgAkAEVrmFw6jlZ14EUcA8gb+UVsImIiNoAw0x7dD0FSNpcbwv1GW0odmr6IfTeR/DguFG8BwwREVk8hpn2QAgg+6RuBiZpi3ELNWRAcCzyAsfgsd+9cEHlgan9gjB/XA8GGSIiahcYZiyVpkZ35119C3WmYUxup7twt3YV6gIo8cCHvyOjuhIDwjywdHI0ZAwyRETUTjDMWBJ1lW7to6Qtt69CbdRCPRpw0K1wXV2jwVP/OYqMG5UI8XTCx4/FwN6W18YQEVH7wTBj7upWoU7eClzcfcsq1O66m9dFxdfbQi2EwGubzuJ4WiFcFbZYM7Mv3J3vsmgkERGRhWGYMUfl+bqZl6StwJW9xqtQ17VQR8YBIYPv2EL9n99S8X1CJuQy4L1p96CLj2sbFE9ERNS2GGbMRVGGbvYlaSuQfsh4FWqPzrrZl7pVqBvRQv1L0jUs/zkJAPA/cd0wLMLHVJUTERFJimFGStdTdNe/JG0Bck4Zj/n1rF3EMQ7wiWpS51Fybgme/yYRQgDTBgRj1qDQVi2biIjInDDMtCUhgOzE2g6krUD+hZsGZbWrUNeeQnIPadaXyC+rxuPrTqBcpcGgzp5YMqk7O5eIiKhdY5gxNa3G0EKdtLWeFuqhuhmYiAmAS8tOBVXXaPDkFwnIKqpEqKcTPvxzH9jZsHOJiIjaN4YZU6ipNm6hrigwjNk56VqnI+OBrmP0LdQtJYTAwo1nkHC1EK4OtvjPzH7o4MTOJSIiav8YZlpLdamudTppS20LdalhrK6FOjIO6DzcJKtQf3LgCjaezIKNXIYP/9wHXXxcWv1rEBERmSOGmZYoL9DNvCRvBS7vBTTVhjHXACByou4U0l1aqFtq17lcvLEjGQCwKL4bhoR7m+xrERERmRuGmZbYsQA4853h82a0ULfU+ewSzP32FIQApg8MwYzYUJN/TSIiInPCMNMSUXHA9WQgapLuY+/INl28Ma+0Ck+sP44KlQb3dvHCP+O7tdnXJiIiMhcMMy0RNQnoNlmSL12l1nUuZRdXoZOXMz6Yxs4lIiKyTvzr1xIS3b9FCIEFP/6BxPQiKB3tsGZWPyid7CSphYiISGoMMxbow32X8dOpbNjIZfjoz30Q5uUsdUlERESSYZixMDvO5uDNnSkAgCWTumNQFy+JKyIiIpIWw4wFOZtVjBe+PQ0AmDUoFI8NbN6SB0RERO0Jw4yFyCupwuzPT6BSrcGQcC+8NjFK6pKIiIjMgknDTGhoKGQymdFjwYIFRtukp6cjPj4ezs7O8PLywvPPPw+VSmW0zZkzZzB06FA4OjqiY8eOWLp0KYQQpizdrFSpNZj9RQJyiqvQ2dsZ70/rA1t2LhEREQFog9bspUuXYvbs2frPXVwMt9nXaDSYOHEivL29cfDgQRQUFGDmzJkQQuC9994DAJSUlGD06NEYPnw4jh8/jgsXLmDWrFlwdnbG/PnzTV2+5IQQ+McPf+B0RhE6ONlhzcx+UDqyc4mIiKiOycOMq6sr/Pz86h3btWsXzp8/j4yMDAQEBAAA3n77bcyaNQvLli2Dm5sbvvrqK1RVVWHdunVQKBSIjo7GhQsXsHr1asybNw8yidqj28r7v17CltPZsJXL8NGfYxDKziUiIiIjJj9X8cYbb8DT0xO9e/fGsmXLjE4hHT58GNHR0fogAwBjx45FdXU1EhIS9NsMHToUCoXCaJvs7GykpaXV+zWrq6tRUlJi9LBEP5/Jwdu7LwAA/nVfNGI7e0pcERERkfkx6czM3//+d/Tp0wfu7u44duwYFi5ciNTUVPznP/8BAOTm5sLX19foNe7u7rC3t0dubq5+m9DQUKNt6l6Tm5uLsLCw277uihUrsGTJEhPsUdvJK6nCyz/+AQD46+AwPNo/WOKKiIiIzFOTZ2YWL15820W9tz5OnDgBAHjhhRcwdOhQ9OzZE0888QQ+/vhjrFmzBgUFBfr3q+80kRDC6Plbt6m7+LehU0wLFy5EcXGx/pGRkdHU3ZTc4i3nUFJVgx4dlXhlQqTU5RAREZmtJs/MzJkzB1OnTr3jNrfOpNQZOHAgAODSpUvw9PSEn58fjh49arRNYWEh1Gq1fvbFz89PP0tTJy8vDwBum9Wpo1AojE5LWZqd53Kx/UwubOQyrHygBzuXiIiI7qDJYcbLywteXs2762xiYiIAwN/fHwAQGxuLZcuWIScnR//crl27oFAoEBMTo9/mlVdegUqlgr29vX6bgICABkOTJSupUuOf/z0LAPjbnzqhe4BS4oqIiIjMm8n+yX/48GG88847OHXqFFJTU/Hdd9/hySefxKRJkxAcrLv+Y8yYMejWrRumT5+OxMRE/PLLL3jxxRcxe/ZsuLm5AQCmTZsGhUKBWbNm4ezZs9i0aROWL1/ebjuZ3vg5GddKqhHq6YS/jwyXuhwiIiKzZ7ILgBUKBb799lssWbIE1dXVCAkJwezZs/HSSy/pt7GxscG2bdvwzDPPYPDgwXB0dMS0adPw1ltv6bdRKpXYvXs3nn32WfTt2xfu7u6YN28e5s2bZ6rSJXMs9Qa+OpoOAFg+pQcc7GwkroiIiMj8yYQV3Eq3pKQESqUSxcXF+hkfc1Ol1mDC//2GK9fLMbVfEFY+0FPqkoiIiCTV2L/fvLLUTHyw9xKuXC+Ht6sCCydw3SUiIqLGYpgxA8m5Jfho32UAwL8md+dyBURERE3AMCMxjVbg5R/PoEYrMLa7L8ZF+0tdEhERkUVhmJHY+kNpOJ1RBFeFLZZOjpa6HCIiIovDMCOhjBsVeGtXCgBg4YQo+Lo5SFwRERGR5WGYkYgQAq/+dBYVKg36h3lgar8gqUsiIiKySAwzEvnvqWwcuHAd9rZyrJjSA3J5+7sBIBERUVtgmJFAQVk1lmw5BwD4+8hwdPZ2kbgiIiIiy8UwI4HXtyWhsEKNSD9X/O1PnaQuh4iIyKIxzLSxfSl52JSYBbkMWPlAT9hxRWwiIqIW4V/SNlReXYNXN+lWxP7L4DD0DuogbUFERETtAMNMG3prVwqyiioR6O6I+WO6Sl0OERFRu8Aw00YS0wux7lAaAGDZ/T3gZG+yBcuJiIisCsNMG1DVaLHgxzMQAphyT0cM7eotdUlERETtBsNMG/hk/2WkXCuFh7M9XovrJnU5RERE7QrDjIldyivDe79eAgAsiu8GD2d7iSsiIiJqXxhmTEirFVi48Q+oNFoMi/DGpF4BUpdERETU7jDMmNDXx9JxPK0QTvY2eP2+aMhkXLKAiIiotTHMmEhucRVW/pwMAPjH2AgEujtJXBEREVH7xDBjAkIIvPbTWZRV16B3UAfMiA2VuiQiIqJ2i2HGBH4+m4s9SddgK5fhjQd6woYrYhMREZkMw0wrK65Q45//1a2I/cywzojwc5W4IiIiovaNYaaVLd+ehPyyanT2dsazI7pIXQ4REVG7xzDTig5dyse3JzIAAG880BMKWxuJKyIiImr/GGZaSZVag4WbzgAApg8MQd9QD4krIiIisg4MM63k3T0XcbWgAn5uDnhpXITU5RAREVkNhplWcDarGP/+7QoA4F/3RcPVwU7iioiIiKwHw0wL1Wi0WLDxD2i0AhN7+mN0N1+pSyIiIrIqDDMt9NnvqTibVQKlox0Wx3eXuhwiIiKrwzDTAlcLyrF69wUAwKsTo+DtqpC4IiIiIuvDMNMCr29LQpVai0GdPfFQTKDU5RAREVklW6kLsGSLJ3WHjUyGhRMiuSI2ERGRRBhmWqBjB0d8PD1G6jKIiIisGk8zERERkUVjmCEiIiKLxjBDREREFo1hhoiIiCwawwwRERFZNIYZIiIismgMM0RERGTRGGaIiIjIojHMEBERkUVjmCEiIiKLxjBDREREFo1hhoiIiCwawwwRERFZNKtYNVsIAQAoKSmRuBIiIiJqrLq/23V/xxtiFWGmtLQUABAUFCRxJURERNRUpaWlUCqVDY7LxN3iTjug1WqRnZ0NV1dXyGSyVn3vkpISBAUFISMjA25ubq363uaA+2f52vs+cv8sX3vfR+5f8wkhUFpaioCAAMjlDV8ZYxUzM3K5HIGBgSb9Gm5ubu3yh7QO98/ytfd95P5Zvva+j9y/5rnTjEwdXgBMREREFo1hhoiIiCwaw0wLKRQKLFq0CAqFQupSTIL7Z/na+z5y/yxfe99H7p/pWcUFwERERNR+cWaGiIiILBrDDBEREVk0hhkiIiKyaAwzREREZNEYZoiIiMiiMczcxbJlyzBo0CA4OTmhQ4cO9W6Tnp6O+Ph4ODs7w8vLC88//zxUKtUd37e6uhrPPfccvLy84OzsjEmTJiEzM9MEe9A0+/btg0wmq/dx/PjxBl83a9as27YfOHBgG1beeKGhobfVumDBgju+RgiBxYsXIyAgAI6Ojhg2bBjOnTvXRhU3XlpaGh5//HGEhYXB0dERnTt3xqJFi+7682jux+/DDz9EWFgYHBwcEBMTg99+++2O2+/fvx8xMTFwcHBAp06d8PHHH7dRpU2zYsUK9OvXD66urvDx8cF9992HlJSUO76mof9Hk5OT26jqplm8ePFttfr5+d3xNZZy/ID6f5/IZDI8++yz9W5v7sfvwIEDiI+PR0BAAGQyGX766Sej8eb+Lvzxxx/RrVs3KBQKdOvWDZs2bWrVuhlm7kKlUuGhhx7C008/Xe+4RqPBxIkTUV5ejoMHD2LDhg348ccfMX/+/Du+79y5c7Fp0yZs2LABBw8eRFlZGeLi4qDRaEyxG402aNAg5OTkGD2eeOIJhIaGom/fvnd87bhx44xet3379jaquumWLl1qVOtrr712x+1XrVqF1atX4/3338fx48fh5+eH0aNH6xcxNRfJycnQarX45JNPcO7cObzzzjv4+OOP8corr9z1teZ6/L799lvMnTsXr776KhITEzFkyBCMHz8e6enp9W6fmpqKCRMmYMiQIUhMTMQrr7yC559/Hj/++GMbV353+/fvx7PPPosjR45g9+7dqKmpwZgxY1BeXn7X16akpBgdr/Dw8DaouHm6d+9uVOuZM2ca3NaSjh8AHD9+3Gjfdu/eDQB46KGH7vg6cz1+5eXl6NWrF95///16x5vzu/Dw4cN45JFHMH36dJw+fRrTp0/Hww8/jKNHj7Ze4YIaZe3atUKpVN72/Pbt24VcLhdZWVn657755huhUChEcXFxve9VVFQk7OzsxIYNG/TPZWVlCblcLnbs2NHqtbeESqUSPj4+YunSpXfcbubMmWLy5MltU1QLhYSEiHfeeafR22u1WuHn5ydWrlypf66qqkoolUrx8ccfm6DC1rVq1SoRFhZ2x23M+fj1799fPPXUU0bPRUZGigULFtS7/UsvvSQiIyONnnvyySfFwIEDTVZja8nLyxMAxP79+xvcZu/evQKAKCwsbLvCWmDRokWiV69ejd7eko+fEEL8/e9/F507dxZarbbecUs6fgDEpk2b9J8393fhww8/LMaNG2f03NixY8XUqVNbrVbOzLTQ4cOHER0djYCAAP1zY8eORXV1NRISEup9TUJCAtRqNcaMGaN/LiAgANHR0Th06JDJa26KzZs3Iz8/H7Nmzbrrtvv27YOPjw+6du2K2bNnIy8vz/QFNtMbb7wBT09P9O7dG8uWLbvjaZjU1FTk5uYaHS+FQoGhQ4ea3fGqT3FxMTw8PO66nTkeP5VKhYSEBKPvPQCMGTOmwe/94cOHb9t+7NixOHHiBNRqtclqbQ3FxcUA0Kjjdc8998Df3x8jR47E3r17TV1ai1y8eBEBAQEICwvD1KlTceXKlQa3teTjp1Kp8OWXX+Kvf/0rZDLZHbe1pONXp7m/Cxs6pq35+5NhpoVyc3Ph6+tr9Jy7uzvs7e2Rm5vb4Gvs7e3h7u5u9Lyvr2+Dr5HKmjVrMHbsWAQFBd1xu/Hjx+Orr77Cr7/+irfffhvHjx/HiBEjUF1d3UaVNt7f//53bNiwAXv37sWcOXPw7rvv4plnnmlw+7pjcutxNsfjdavLly/jvffew1NPPXXH7cz1+OXn50Oj0TTpe1/f/5O+vr6oqalBfn6+yWptKSEE5s2bh3vvvRfR0dENbufv749PP/0UP/74IzZu3IiIiAiMHDkSBw4caMNqG2/AgAH4/PPPsXPnTvz73/9Gbm4uBg0ahIKCgnq3t9TjBwA//fQTioqK7viPP0s7fjdr7u/Cho5pa/7+tG21d7IgixcvxpIlS+64zfHjx+96jUid+hK4EOKuybw1XtNYzdnnzMxM7Ny5E999991d3/+RRx7RfxwdHY2+ffsiJCQE27Ztw5QpU5pfeCM1Zf9eeOEF/XM9e/aEu7s7HnzwQf1sTUNuPTamPF63as7xy87Oxrhx4/DQQw/hiSeeuONrpT5+d9PU731929f3vDmZM2cO/vjjDxw8ePCO20VERCAiIkL/eWxsLDIyMvDWW2/hT3/6k6nLbLLx48frP+7RowdiY2PRuXNnrF+/HvPmzav3NZZ4/ADdP/7Gjx9vNFN/K0s7fvVpzu9CU//+tMowM2fOHEydOvWO24SGhjbqvfz8/G67iKmwsBBqtfq2JHrza1QqFQoLC41mZ/Ly8jBo0KBGfd2mas4+r127Fp6enpg0aVKTv56/vz9CQkJw8eLFJr+2OVpyTOu6di5dulRvmKnrvMjNzYW/v7/++by8vAaPcWtr6v5lZ2dj+PDhiI2Nxaefftrkr9fWx68hXl5esLGxue1fcHf63vv5+dW7va2t7R3DqpSee+45bN68GQcOHEBgYGCTXz9w4EB8+eWXJqis9Tk7O6NHjx4N/mxZ4vEDgKtXr2LPnj3YuHFjk19rKcevub8LGzqmrfn70yrDjJeXF7y8vFrlvWJjY7Fs2TLk5OToD+6uXbugUCgQExNT72tiYmJgZ2eH3bt34+GHHwYA5OTk4OzZs1i1alWr1HWrpu6zEAJr167FjBkzYGdn1+SvV1BQgIyMDKMfeFNqyTFNTEwEgAZrDQsLg5+fH3bv3o177rkHgO7c+P79+/HGG280r+Amasr+ZWVlYfjw4YiJicHatWshlzf9bHJbH7+G2NvbIyYmBrt378b999+vf3737t2YPHlyva+JjY3Fli1bjJ7btWsX+vbt26yfZVMSQuC5557Dpk2bsG/fPoSFhTXrfRITEyU/Vo1VXV2NpKQkDBkypN5xSzp+N1u7di18fHwwceLEJr/WUo5fc38XxsbGYvfu3Uaz4rt27Wrdf7y32qXE7dTVq1dFYmKiWLJkiXBxcRGJiYkiMTFRlJaWCiGEqKmpEdHR0WLkyJHi5MmTYs+ePSIwMFDMmTNH/x6ZmZkiIiJCHD16VP/cU089JQIDA8WePXvEyZMnxYgRI0SvXr1ETU1Nm+9jffbs2SMAiPPnz9c7HhERITZu3CiEEKK0tFTMnz9fHDp0SKSmpoq9e/eK2NhY0bFjR1FSUtKWZd/VoUOHxOrVq0ViYqK4cuWK+Pbbb0VAQICYNGmS0XY3758QQqxcuVIolUqxceNGcebMGfHoo48Kf39/s9u/rKws0aVLFzFixAiRmZkpcnJy9I+bWdLx27Bhg7CzsxNr1qwR58+fF3PnzhXOzs4iLS1NCCHEggULxPTp0/XbX7lyRTg5OYkXXnhBnD9/XqxZs0bY2dmJH374QapdaNDTTz8tlEql2Ldvn9Gxqqio0G9z6/698847YtOmTeLChQvi7NmzYsGCBQKA+PHHH6XYhbuaP3++2Ldvn7hy5Yo4cuSIiIuLE66uru3i+NXRaDQiODhYvPzyy7eNWdrxKy0t1f+dA6D/fXn16lUhRON+F06fPt2o2/D3338XNjY2YuXKlSIpKUmsXLlS2NraiiNHjrRa3QwzdzFz5kwB4LbH3r179dtcvXpVTJw4UTg6OgoPDw8xZ84cUVVVpR9PTU297TWVlZVizpw5wsPDQzg6Ooq4uDiRnp7ehnt2Z48++qgYNGhQg+MAxNq1a4UQQlRUVIgxY8YIb29vYWdnJ4KDg8XMmTPNan/qJCQkiAEDBgilUikcHBxERESEWLRokSgvLzfa7ub9E0LXkrho0SLh5+cnFAqF+NOf/iTOnDnTxtXf3dq1a+v9eb313y2Wdvw++OADERISIuzt7UWfPn2MWpdnzpwphg4darT9vn37xD333CPs7e1FaGio+Oijj9q44sZp6Fjd/LN36/698cYbonPnzsLBwUG4u7uLe++9V2zbtq3ti2+kRx55RPj7+ws7OzsREBAgpkyZIs6dO6cft+TjV2fnzp0CgEhJSbltzNKOX13r+K2PmTNnCiEa97tw6NCh+u3rfP/99yIiIkLY2dmJyMjIVg9vMiFqr6wiIiIiskBszSYiIiKLxjBDREREFo1hhoiIiCwawwwRERFZNIYZIiIismgMM0RERGTRGGaIiIjIojHMEBERkUVjmCEiIiKLxjBDREREFo1hhoiIiCza/wP+qAL1CuvawQAAAABJRU5ErkJggg=="
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 43
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "sin cos",
   "id": "1b87e82526ccb57f"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-06-24T07:32:52.479486Z",
     "start_time": "2025-06-24T07:32:52.425346Z"
    }
   },
   "cell_type": "code",
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "x=np.linspace(-4*np.pi,4*np.pi,100)\n",
    "y=np.sin(x)\n",
    "y_1= np.cos(x)\n",
    "plt.figure(figsize=(8,1))\n",
    "plt.title(\"sin cos\")\n",
    "\n",
    "plt.plot(x,y)\n",
    "plt.plot(x,y_1)\n",
    "plt.show()"
   ],
   "id": "4551d7714941dd3c",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 800x100 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 53
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "sigmoid函数 激化函数 激励函数",
   "id": "4753e3303bfa31d2"
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "",
   "id": "97fb16e5dfb350b6"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-06-24T08:30:39.951751Z",
     "start_time": "2025-06-24T08:30:39.572293Z"
    }
   },
   "cell_type": "code",
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "x=np.linspace(-20,20,50)\n",
    "y=1/(1+np.exp(-x))\n",
    "plt.title(\"xxx\")\n",
    "plt.plot(x,y,color='red')\n",
    "plt.savefig(\"xxx.png\")\n",
    "plt.show()"
   ],
   "id": "63b1f0ae80b3d4cd",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 1
  },
  {
   "metadata": {},
   "cell_type": "code",
   "outputs": [],
   "execution_count": null,
   "source": "噪声函数",
   "id": "89dd16457d28c276"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-06-25T00:40:48.413466Z",
     "start_time": "2025-06-25T00:40:48.346124Z"
    }
   },
   "cell_type": "code",
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "x=np.linspace(-50,50,16)\n",
    "y=13.4*x+38\n",
    "np.random.seed(8888)\n",
    "y_1= 13.4*x+38+(np.random.rand(16)-0.5)*500\n",
    "plt.title(\"xxx\")\n",
    "# plt.scatter(x,y)\n",
    "plt.scatter(x,y_1)\n",
    "plt.show()"
   ],
   "id": "1b350361a890bfef",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 2
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
